Gergely
If a system would tell you when you are getting "dangerously close to the limits" but wouldn't restrict you in anyway, that would be an extra layer of protection.
Let me give you an example of one of these extra layers that already exist. You have experience of the "amateur side" - how do you know when you are getting close to the IAS limit for your aircraft? You look at the ASI and compare the needle position with the limit mark on the scale. You then use pilot judgement to assess how soon you will reach the limit, and whether you need to take action.
In a modern cockpit such as the Airbus FBW, the ASI has a "speed trend" indication in the form of a yellow arrow extending up or down from the present speed. If the speed is steady the arrow does not show. If the speed is changing the length of the arrow shows you how quickly the change is happening, and predicts what the a/c speed will be in 10 seconds. So in this FBW cockpit the pilot has a visual 10 seconds warning before reaching the limit, and before the next protection becomes necessary. This is plenty of time to take action.
Regarding weather radar, in most cases the pilot will have 20 minutes warning of storms - why do you need more?
Regarding changes of flight control laws - the a/c cannot predict that this will be necessary, because the change is not necessary until a failure occurs. So no advance warning is possible.